In a competitive market, if both demand and supply curves are linear, then a per-unit tax of $10 will generate exactly the same deadweight loss as a per-unit subsidy of $10.

This statement is true. In a competitive market, a per-unit tax and a per-unit subsidy of equal amounts will have equal but opposite effects on the equilibrium quantity and price. However, the deadweight loss generated by either policy will depend on the elasticity of both demand and supply. If both curves are linear, the deadweight loss will be equal for both policies.